The present invention relates to tooth profiles of a rigid internal gear and a flexible external gear of a wave gear drive. More particularly, this relates to tooth profiles applied to both gears to avoid superimposition of bending stress produced by elliptical deformation of the rim of the flexible external gear in the vicinity of the major axis and rim tensile stress produced by the load on the tooth surface, and to equalize and reduce stress on the tooth bottom rim of the flexible external gear and wave generator ball load.
A typical wave gear drive has a rigid circular internal gear, a cup-shaped flexible external gear disposed inside the rigid internal gear, and a wave generator that flexes the flexible external gear into an elliptical shape to mesh the two gears at each end of the elliptical major axis and rotates the mesh portions in the circumferential direction. The cup-shaped flexible external gear comprises a flexible cylindrical body, an annular diaphragm formed continuously with one end of the cylindrical body to extend radially inward, an annular boss formed integrally with the center of the diaphragm, and external teeth formed on the outer periphery at the other end of the cylindrical body.
The wave generator has an elliptical profile and is located inside the cylindrical body on which the external teeth are formed, producing a state in which the portion on which the external teeth are formed is flexed into an elliptical shape. Therefore, the cylindrical body is flexed into an elliptical shape with the amount of flexing from the diaphragm side toward the open end on which the external teeth are formed being approximately proportional to the distance from the diaphragm. The difference in the number of teeth the two gears have is 2n (n: positive integer); the difference is normally two teeth.
When the wave generator is rotated at high speed by a motor or the like, the mesh portions of the two gears are moved in the circumferential direction, and the rotation, the speed of which is greatly reduced in accordance with the difference in the number of teeth the two gears have, is taken off from the flexible external gear or rigid internal gear.
Here, the flexible external gear is what is known as a silk-hat-shaped flexible external gear. This flexible external gear has a configuration in which, from the one end of the cylindrical body, the annular diaphragm widens in a radially outward direction, and a thick, annular boss is formed integrally on the outer edge of the diaphragm. In this case, the cylindrical body is flexed into an elliptical shape with the amount of flexing produced from the diaphragm side toward the open end on which the external teeth are formed being approximately proportional to the distance from the diaphragm.
Since the invention by C. W. Musser (U.S. Pat. No. 2,906,143), the original inventor of the wave gear drive, there have been various inventions by many researchers, including Musser and the present inventor. Even with respect just to the tooth profiles, there are various inventions. Among these, the present inventor proposed a method of designing a tooth profile in which the addendum profiles for wide contact between the rigid internal gear and flexible external gear are derived using a rack approximation of the meshing between the two gears. Since then, too, the present inventor and other researchers have made many inventions relating to tooth profiles.
At present there is a strong market demand for wave gear drives having improved performance. Especially, improved load capabilities are desired. The main elements governing load capabilities of wave gear drives are the tooth bottom rim of the flexible external gear and the inner rolling contact surface of the wave generator, particularly the fatigue strength at locations in the vicinity of the major axis thereof. The object of the present invention is to reduce the stresses produced at these two locations.
The present invention uses the following two techniques to attain the above object. The first is, with respect to realizing continuous meshing in the direction of the tooth trace of unmodified spur gears used in a cup-shaped or silk-hat-shaped flexible external gear, which hitherto has been considered impossible, to reduce the tooth bottom rim stress by extending the tooth contact in the direction of the tooth trace, by setting the pressure angle according to the main meshing point and amount of flexing of the flexible external gear.
The second is, at the meshing between the teeth of the two gears in a section perpendicular to the flexible external gear axis (principal section) selected at an arbitrary point in a direction of the tooth trace, with the flexing of the flexible external gear reduced from the normal to a negative deviation the main part of the tooth meshing region separates from the vicinity of the major axis of the ellipse, and by applying the Euler-Savary equation established at the variable speed ratio gear to the tooth profile design, continuous contact of tooth profiles in the principal section is realized.
By using the two techniques in combination, the present invention prevents superimposition of bending stress produced by elliptical deformation of the rim of the flexible external gear in the vicinity of the major axis and rim tensile stress produced by the load on the tooth surfaces, and helps to equalize and reduce stress on the tooth bottom rim of the flexible external gear and wave generator ball load.
A wave gear drive having a rigid internal gear, a cup-shaped or silk-hat-shaped flexible external gear disposed inside the rigid internal gear, and a wave generator that flexes sections of the flexible external gear perpendicular to an axis thereof into an elliptical shape such that the amount of flexing increases from a diaphragm side thereof toward an opening portion thereof approximately in proportion to distance from the diaphragm, and rotates that shape, the rotation of the wave generator producing relative rotation between the two gears, wherein a main portion of the tooth profiles of the two gears is defined as follows.
First, the basic flexible external gear and rigid internal gear are both spur gears and a number of teeth of the flexible external gear is defined as 2n (where n is a positive integer) fewer than a number of teeth of the rigid internal gear.
Also, with a principal section defined as a section perpendicular to the flexible external gear selected at an arbitrary point in the direction of the tooth trace, in this principal section, taking as a teeth-meshing center position a position on a neutral line of the elliptical rim of the flexible external gear away from the major axis, by assigning xcex8 as the angle of inclination of a tangent with that position along the neutral line of the rim, zF, zC as the number of teeth on the flexible external gear and rigid internal gear, respectively, ro, rn as, respectively, the diameter of the pitch circle of the flexible external gear and the radius of the neutral curve of the rim prior to deformation and the amount of flexing of the principal section as w in Equation (4)                                                         w              =                            ⁢                                                                    -                    b                                    -                                                                                    b                        2                                            -                                              4                        ⁢                        ac                                                                                                              2                  ⁢                  a                                                                                                        a              =                            ⁢                                                                    3                    ⁢                                          z                      F                                                                            r                    n                                                  ⁢                cos                ⁢                                  xe2x80x83                                ⁢                                  (                                      2                    ⁢                    θ                                    )                                                                                                        b              =                            ⁢                                                z                  C                                -                                  z                  F                                +                                  3                  ⁢                                      z                    F                                    ⁢                                                            r                      o                                                              r                      n                                                        ⁢                                                            cos                      2                                        ⁡                                          (                                              2                        ⁢                        θ                                            )                                                                      -                                                      z                    C                                    ⁢                                                            1                      +                                              3                        ⁢                                                                              cos                            2                                                    ⁡                                                      (                                                          2                              ⁢                              θ                                                        )                                                                                                                                xc3x97                                                                                                                      ⁢                              [                                                      2                    ⁢                    sin                    ⁢                                          {                                                                                                    tan                                                          -                              1                                                                                ⁡                                                      (                                                                                          cot                                3                                                            ⁢                              θ                                                        )                                                                          +                        θ                                            }                                                        -                                                            sin                      ⁡                                              (                                                  2                          ⁢                          θ                                                )                                                              ⁢                    cos                    ⁢                                          {                                                                                                    tan                                                          -                              1                                                                                ⁡                                                      (                                                                                          cot                                3                                                            ⁢                              θ                                                        )                                                                          -                        θ                                            }                                                                      ]                                                                                        c              =                            ⁢                                                                    r                    o                                    ⁡                                      (                                                                  z                        C                                            -                                              z                        F                                                              )                                                  ⁢                                  cos                  ⁡                                      (                                          2                      ⁢                      θ                                        )                                                                                                          (        4        )            
tangential direction common to both tooth profiles at the point of the contact between the tooth profiles of the two gears at the center position of the main meshing region within the principal section is made to coincide with the tangential direction at the said point of the contact of the curves of the linear generatrix of the neutral cylindrical plane of the rim projected on the principal section, effecting continuous contact in the tooth trace direction.
The center of the radius of curvature of each of the two tooth profiles at the point of the meshing contact in the principal section is set based on the Euler-Savary equation established at the variable speed ratio gear.
Thereby, a state of continuous meshing of the tooth profiles is formed at the principal section of the flexible external gear, at a meshing region away from the major axis.
With respect to the tooth profiles at the sections perpendicular to the axes of the two gears, when the main part of the concave tooth profile of the rigid internal gear is given an involute curvature and the main part of the convex tooth profile of the flexible external gear is an arc, the radius of the arc can be set at up to a radius of curvature determined by the Euler-Savary equation established at the variable speed ratio gear in the principal section.
Also with respect to the tooth profiles at the sections perpendicular to the axes of the two gears, when the main part of the concave tooth profile of the rigid internal gear and the main part of the convex tooth profile of the flexible external gear are both formed as arcs, the radius of the concave tooth profile of the rigid internal gear can be set at or above, and the radius of the convex tooth profile of the flexible external gear can be set at or below, the radius of curvature of the arc radii determined by the Euler-Savary equation established at the variable speed ratio gear in the principal section.